ar X iv : 0 70 7 . 45 25 v 1 [ m at h . A G ] 3 1 Ju l 2 00 7 Analytic Classification of Plane Branches up to Multiplicity 4

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES

ar X iv : 0 70 7 . 39 09 v 1 [ m at h - ph ] 2 6 Ju l 2 00 7 Schrödinger operators on armchair nanotubes . I

We consider the Schrödinger operator with a periodic potential on quasi-1D models of armchair single-wall nanotubes. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite number of eigenvalues with infinite multiplicity. We describe all eigenfunctions with the same eigenvalue. We define a Lyapunov function, which is analytic on so...

ar X iv : 0 70 7 . 19 46 v 1 [ m at h . D G ] 1 3 Ju l 2 00 7 The uniqueness of the helicoid in the Lorentz - Minkowski space

We prove that the Lorentzian helicoid and Enneper’s surface are the unique properly embedded maximal surfaces bounded by a lightlike regular arc of mirror symmetry.

ar X iv : 0 70 7 . 42 19 v 1 [ m at h . D G ] 2 8 Ju l 2 00 7 Real embeddings , η - invariant and Chern - Simons current ∗

We present an alternate proof of the Bismut-Zhang localization formula for η-invariants without using the analytic techniques developed by Bismut-Lebeau. A Riemann-Roch property for Chern-Simons currents, which is of independent interest, is established in due course.

ar X iv : 0 70 7 . 40 46 v 1 [ m at h . A G ] 2 7 Ju l 2 00 7 CLIFFORD ’ S THEOREM FOR COHERENT SYSTEMS

Let C be an algebraic curve of genus g ≥ 2. We prove an analogue of Clifford’s theorem for coherent systems on C and some refinements using results of Re and Mercat.